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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class DFP</h1><p class="nomargin-top"><span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP">source&nbsp;code</a></span></p>
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DFP (<em>Davidon-Fletcher-Powell</em>) search

<!-- ==================== INSTANCE METHODS ==================== -->
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      <span class="summary-type">&nbsp;</span>
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          <td><span class="summary-sig"><a href="peach.optm.quasinewton.DFP-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">f</span>,
        <span class="summary-sig-arg">x0</span>,
        <span class="summary-sig-arg">ranges</span>=<span class="summary-sig-default">None</span>,
        <span class="summary-sig-arg">df</span>=<span class="summary-sig-default">None</span>,
        <span class="summary-sig-arg">h</span>=<span class="summary-sig-default">0.1</span>,
        <span class="summary-sig-arg">emax</span>=<span class="summary-sig-default">1e-08</span>,
        <span class="summary-sig-arg">imax</span>=<span class="summary-sig-default">1000</span>)</span><br />
      Initializes the optimizer.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.__init__">source&nbsp;code</a></span>
            
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    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
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        <tr>
          <td><span class="summary-sig"><a name="__get_x"></a><span class="summary-sig-name">__get_x</span>(<span class="summary-sig-arg">self</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.__get_x">source&nbsp;code</a></span>
            
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      <span class="summary-type">&nbsp;</span>
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          <td><span class="summary-sig"><a name="__set_x"></a><span class="summary-sig-name">__set_x</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">x0</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.__set_x">source&nbsp;code</a></span>
            
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
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          <td><span class="summary-sig"><a href="peach.optm.quasinewton.DFP-class.html#restart" class="summary-sig-name">restart</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">x0</span>,
        <span class="summary-sig-arg">h</span>=<span class="summary-sig-default">None</span>)</span><br />
      Resets the optimizer, returning to its original state, and allowing to
use a new first estimate.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.restart">source&nbsp;code</a></span>
            
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      <span class="summary-type">&nbsp;</span>
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          <td><span class="summary-sig"><a href="peach.optm.quasinewton.DFP-class.html#step" class="summary-sig-name">step</a>(<span class="summary-sig-arg">self</span>)</span><br />
      One step of the search.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.step">source&nbsp;code</a></span>
            
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    </td>
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    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="peach.optm.quasinewton.DFP-class.html#__call__" class="summary-sig-name">__call__</a>(<span class="summary-sig-arg">self</span>)</span><br />
      Transparently executes the search until the minimum is found. The stop
criteria are the maximum error or the maximum number of iterations,
whichever is reached first. Note that this is a <tt class="rst-docutils literal">__call__</tt> method, so
the object is called as a function. This method returns a tuple
<tt class="rst-docutils literal">(x, e)</tt>, with the best estimate of the minimum and the error.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.__call__">source&nbsp;code</a></span>
            
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    <td colspan="2" class="summary">
    <p class="indent-wrapped-lines"><b>Inherited from <code>object</code></b>:
      <code>__delattr__</code>,
      <code>__format__</code>,
      <code>__getattribute__</code>,
      <code>__hash__</code>,
      <code>__new__</code>,
      <code>__reduce__</code>,
      <code>__reduce_ex__</code>,
      <code>__repr__</code>,
      <code>__setattr__</code>,
      <code>__sizeof__</code>,
      <code>__str__</code>,
      <code>__subclasshook__</code>
      </p>
    </td>
  </tr>
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<!-- ==================== INSTANCE VARIABLES ==================== -->
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="ranges"></a><span class="summary-name">ranges</span><br />
      Holds the ranges for every variable. Although it is a writable
property, care should be taken in changing parameters before ending the
convergence.
    </td>
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<!-- ==================== PROPERTIES ==================== -->
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      <span class="summary-type">&nbsp;</span>
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        <a href="peach.optm.quasinewton.DFP-class.html#x" class="summary-name">x</a><br />
      The estimate of the position of the minimum.
    </td>
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    <td colspan="2" class="summary">
    <p class="indent-wrapped-lines"><b>Inherited from <code>object</code></b>:
      <code>__class__</code>
      </p>
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<!-- ==================== METHOD DETAILS ==================== -->
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<a name="__init__"></a>
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<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">__init__</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">f</span>,
        <span class="sig-arg">x0</span>,
        <span class="sig-arg">ranges</span>=<span class="sig-default">None</span>,
        <span class="sig-arg">df</span>=<span class="sig-default">None</span>,
        <span class="sig-arg">h</span>=<span class="sig-default">0.1</span>,
        <span class="sig-arg">emax</span>=<span class="sig-default">1e-08</span>,
        <span class="sig-arg">imax</span>=<span class="sig-default">1000</span>)</span>
    <br /><em class="fname">(Constructor)</em>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.__init__">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Initializes the optimizer.</p>
<p>To create an optimizer of this type, instantiate the class with the
parameters given below:</p>
  <dl class="fields">
    <dt>Parameters:</dt>
    <dd><ul class="nomargin-top">
        <li><strong class="pname"><code>f</code></strong> - A multivariable function to be optimized. The function should have
only one parameter, a multidimensional line-vector, and return the
function value, a scalar.</li>
        <li><strong class="pname"><code>x0</code></strong> - First estimate of the minimum. Estimates can be given in any format,
but internally they are converted to a one-dimension vector, where
each component corresponds to the estimate of that particular
variable. The vector is computed by flattening the array.</li>
        <li><strong class="pname"><code>ranges</code></strong> - A range of values might be passed to the algorithm, but it is not
necessary. If supplied, this parameter should be a list of ranges
for each variable of the objective function. It is specified as a
list of tuples of two values, <tt class="rst-docutils literal">(x0, x1)</tt>, where <tt class="rst-docutils literal">x0</tt> is the
start of the interval, and <tt class="rst-docutils literal">x1</tt> its end. Obviously, <tt class="rst-docutils literal">x0</tt> should
be smaller than <tt class="rst-docutils literal">x1</tt>. It can also be given as a list with a simple
tuple in the same format. In that case, the same range will be
applied for every variable in the optimization.</li>
        <li><strong class="pname"><code>df</code></strong> - A function to calculate the gradient vector of the cost function
<tt class="rst-docutils literal">f</tt>. Defaults to <tt class="rst-docutils literal">None</tt>, if no gradient is supplied, then it is
estimated from the cost function using Euler equations.</li>
        <li><strong class="pname"><code>h</code></strong> - Convergence step. This method does not takes into consideration the
possibility of varying the convergence step, to avoid Stiefel cages.</li>
        <li><strong class="pname"><code>emax</code></strong> - Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.</li>
        <li><strong class="pname"><code>imax</code></strong> - Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.</li>
    </ul></dd>
    <dt>Overrides:
        object.__init__
    </dt>
  </dl>
</td></tr></table>
</div>
<a name="restart"></a>
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       cellspacing="0" width="100%" bgcolor="white">
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  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">restart</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">x0</span>,
        <span class="sig-arg">h</span>=<span class="sig-default">None</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.restart">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Resets the optimizer, returning to its original state, and allowing to
use a new first estimate.
  <dl class="fields">
    <dt>Parameters:</dt>
    <dd><ul class="nomargin-top">
        <li><strong class="pname"><code>x0</code></strong> - New estimate of the minimum. Estimates can be given in any format,
but internally they are converted to a one-dimension vector, where
each component corresponds to the estimate of that particular
variable. The vector is computed by flattening the array.</li>
        <li><strong class="pname"><code>h</code></strong> - Convergence step. This method does not takes into consideration the
possibility of varying the convergence step, to avoid Stiefel cages.</li>
    </ul></dd>
  </dl>
</td></tr></table>
</div>
<a name="step"></a>
<div>
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       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">step</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.step">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>One step of the search.</p>
<p>In this method, the result of the step is dependent of parameters
calculated before (namely, the estimate of the inverse hessian), so it
is not recomended that different investigations are used with the same
optimizer in the same cost function.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>This method returns a tuple <tt class="rst-docutils literal">(x, e)</tt>, where <tt class="rst-docutils literal">x</tt> is the updated
estimate of the minimum, and <tt class="rst-docutils literal">e</tt> is the estimated error.</dd>
    <dt>Overrides:
        <a href="peach.optm.base.Optimizer-class.html#step">base.Optimizer.step</a>
    </dt>
  </dl>
</td></tr></table>
</div>
<a name="__call__"></a>
<div>
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       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">__call__</span>(<span class="sig-arg">self</span>)</span>
    <br /><em class="fname">(Call operator)</em>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.optm.quasinewton-pysrc.html#DFP.__call__">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Transparently executes the search until the minimum is found. The stop
criteria are the maximum error or the maximum number of iterations,
whichever is reached first. Note that this is a <tt class="rst-rst-docutils literal rst-docutils literal">__call__</tt> method, so
the object is called as a function. This method returns a tuple
<tt class="rst-rst-docutils literal rst-docutils literal">(x, e)</tt>, with the best estimate of the minimum and the error.
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>This method returns a tuple <tt class="rst-docutils literal">(x, e)</tt>, where <tt class="rst-docutils literal">x</tt> is the best
estimate of the minimum, and <tt class="rst-docutils literal">e</tt> is the estimated error.</dd>
    <dt>Overrides:
        <a href="peach.optm.base.Optimizer-class.html#__call__">base.Optimizer.__call__</a>
    </dt>
  </dl>
</td></tr></table>
</div>
<br />
<!-- ==================== PROPERTY DETAILS ==================== -->
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      <tr valign="top">
        <td align="left"><span class="table-header">Property Details</span></td>
        <td align="right" valign="top"
         ><span class="options">[<a href="#section-PropertyDetails"
         class="privatelink" onclick="toggle_private();"
         >hide private</a>]</span></td>
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<a name="x"></a>
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<tr><td>
  <h3 class="epydoc">x</h3>
  The estimate of the position of the minimum.
  <dl class="fields">
    <dt>Get Method:</dt>
    <dd class="value"><span class="summary-sig"><a href="peach.optm.quasinewton.DFP-class.html#__get_x" class="summary-sig-name" onclick="show_private();">__get_x</a>(<span class="summary-sig-arg">self</span>)</span>
    </dd>
    <dt>Set Method:</dt>
    <dd class="value"><span class="summary-sig"><a href="peach.optm.quasinewton.DFP-class.html#__set_x" class="summary-sig-name" onclick="show_private();">__set_x</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">x0</span>)</span>
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